论文标题
跑步粒子的职业时间与重置
Occupation time of a run-and-tumble particle with resetting
论文作者
论文摘要
我们研究经过随机重置的跑步粒子（RTP）的正占用时间。在重置协议下，粒子的位置以随机的时间序列重置为原始序列，该序列由带价$ r $的泊松过程生成。带固定概率$ρ_1$和$ρ_ { - 1} =1-ρ_1$的速度状态重置为$ \ pm v $，其中$ v $是速度。我们利用这样一个事实，即在有或没有重置的情况下生成函数与续订方程相关，并且可以通过求解相应的FEYNMAN-KAC方程来计算后者生成函数。这使我们能够在拉普拉斯空间中定位于当时生成函数的最大真实极点，从而使用Gartner-ellis定理得出了用于职业时间概率密度的大偏差原理（LDP）。我们探讨了南股自行社如何取决于速度状态的开关率$α$，重置率$ r $和概率$ρ_1$。特别是，我们表明，在快速开关限制$α\ rightarrow \ infty $中恢复了带有重置的布朗粒子的相应LDP。另一方面，慢速开关限制中的行为取决于重置协议中的$ρ_1$。
We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times that is generated by a Poisson process with rate $r$. The velocity state is reset to $\pm v$ with fixed probabilities $ρ_1$ and $ρ_{-1}=1-ρ_1$, where $v$ is the speed. We exploit the fact that the moment generating functions with and without resetting are related by a renewal equation, and the latter generating function can be calculated by solving a corresponding Feynman-Kac equation. This allows us to numerically locate in Laplace space the largest real pole of the moment generating function with resetting, and thus derive a large deviation principle (LDP) for the occupation time probability density using the Gartner-Ellis theorem. We explore how the LDP depends on the switching rate $α$ of the velocity state, the resetting rate $r$ and the probability $ρ_1$. In particular, we show that the corresponding LDP for a Brownian particle with resetting is recovered in the fast switching limit $α\rightarrow \infty$. On the other hand, the behavior in the slow switching limit depends on $ρ_1$ in the resetting protocol.
